Begin cooking the rice according to the package directions.
To make the sauce, stir all of the ingredients together in a small bowl.
To cook the tofu, coat the bottom of a large nonstick skillet with the vegetable oil and place it over medium heat. Give the oil a minute to heat up, then add the tofu cubes, spreading them out in a single layer. Cook the tofu for about 10 minutes, flipping the pieces halfway through, until browned and crispy.
While the tofu cooks, stir the soy sauce, toasted sesame oil, and brown sugar together in a small bowl or cup. After the tofu has browned, drizzle the soy sauce mixture over the tofu, then flip the pieces a few times to coat them in the sauce. Cook them for a minute or two longer, until most of the liquid has dried up. Remove the tofu from the skillet and transfer it to a plate.
Place a small pot of water over high heat. Let it come to a boil while you cook the vegetables. You'll use it later to blanch the bean sprouts.
Add a tablespoon of vegetable oil to the skillet and raise the heat to medium-high. Give it a minute to heat up, then add the sliced mushrooms and sprinkle them with a pinch of salt. Cook the mushrooms for about 4 minutes, flipping them halfway through, until tender and browned. Add about a clove of minced garlic (you can eyeball the amount if you've minced all of your garlic cloves together) and drizzle the mushrooms with a teaspoon of sesame oil. Cook about 30 seconds longer, while stirring, then transfer them to a plate.
Heat another teaspoon of vegetable oil in the skillet, then add the carrots and a pinch of salt. Cook the carrots for about 2 minutes, stirring occasionally, until bright orange and tender-crisp. Add a clove of the garlic and a teaspoon of sesame oil. Stir and cook 30 seconds more, then transfer the carrots to a plate.
Heat another teaspoon of vegetable oil in the skillet, then add the zucchini and a pinch of salt. Cook the zucchini for about 3 minutes, stirring occasionally, until tender-crisp. Add a clove of garlic and a teaspoon of sesame oil. Cook another 30 seconds, stirring constantly, then move the zucchini to a plate.
Add another teaspoon of oil to the skillet. Once the oil heats up, add the spinach and a pinch of salt. Sauté the spinach for 1 to 2 minutes, just until it wilts, then add garlic and a teaspoon of sesame oil. Continue cooking the spinach for 30 seconds, then transfer it to a plate.
To cook the bean sprouts, take the pot containing the water off the heat, then add the sprouts. Blanch them for about 1 minute, just until they start to soften. Drain them, then rinse them with cold water. Place them in a bowl and toss them with 1 teaspoon of toasted sesame oil and a pinch of salt.
To serve, divide the rice among 4 bowls, then top each bowl with vegetables, tofu, bean sprouts, scallions, and sesame seeds. Drizzle with sauce and enjoy.